Free ergodic Z2-systems and complexity

Cyr Van; Bryna Kra

doi:10.1090/proc/13279

Free ergodic Z²-systems and complexity

Cyr Van, Bryna Kra

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Using results relating the complexity of a two dimensional sub-shift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on [0, 1) which is invariant under both x → px (mod 1) and x → qx (mod 1), showing that any potential counterexample has a nontrivial lower bound on its complexity.

Original language	English (US)
Pages (from-to)	1163-1173
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	3
DOIs	https://doi.org/10.1090/proc/13279
State	Published - 2017

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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title = "Free ergodic Z2-systems and complexity",

abstract = "Using results relating the complexity of a two dimensional sub-shift to its periodicity, we obtain an application to the well-known conjecture of Furstenberg on a Borel probability measure on [0, 1) which is invariant under both x → px (mod 1) and x → qx (mod 1), showing that any potential counterexample has a nontrivial lower bound on its complexity.",

author = "Cyr Van and Bryna Kra",

note = "Funding Information: The second author was partially supported by NSF grant 1500670. Publisher Copyright: {\textcopyright} 2016 American Mathematical Society.",

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Free ergodic Z²-systems and complexity

Abstract

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